15c^2-2d^2-7cd=0

Solution for 15c^2-2d^2-7cd=0 equation:

Simplifying
15c2 + -2d2 + -7cd = 0

Reorder the terms:
-7cd + 15c2 + -2d2 = 0

Solving
-7cd + 15c2 + -2d2 = 0

Solving for variable 'c'.

Factor a trinomial.
(3c + -2d)(5c + d) = 0

Subproblem 1
Set the factor '(3c + -2d)' equal to zero and attempt to solve:

Simplifying
3c + -2d = 0

Solving
3c + -2d = 0

Move all terms containing c to the left, all other terms to the right.

Add '2d' to each side of the equation.
3c + -2d + 2d = 0 + 2d

Combine like terms: -2d + 2d = 0
3c + 0 = 0 + 2d
3c = 0 + 2d
Remove the zero:
3c = 2d

Divide each side by '3'.
c = 0.6666666667d

Simplifying
c = 0.6666666667d
Subproblem 2
Set the factor '(5c + d)' equal to zero and attempt to solve:

Simplifying
5c + d = 0

Solving
5c + d = 0

Move all terms containing c to the left, all other terms to the right.

Add '-1d' to each side of the equation.
5c + d + -1d = 0 + -1d

Combine like terms: d + -1d = 0
5c + 0 = 0 + -1d
5c = 0 + -1d
Remove the zero:
5c = -1d

Divide each side by '5'.
c = -0.2d

Simplifying
c = -0.2d
Solution
c = {0.6666666667d, -0.2d}